Scientists delight in extracting order from chaos—finding patterns in the complexity of the real world that pull back the curtain and reveal how things work. Sometimes, though, those patterns create more head-scratching than excitement. Such is the case with Benford’s law. One might expect a collection of real-world data—say, the half-lives of various isotopes, for example—to pretty much look like random numbers. And one might further expect the first (non-zero) digit of each of those numbers to also be random (i.e. just as many 2s as 9s).
Oddly, one would (in many cases) be wrong. It turns out that 1s are more likely than 2s, which are more likely than 3s, and so on. Not only that, the probabilities match a logarithmic distribution, just like the spacing on a logarithmic scale. The number 1 will be the first digit about 30 percent of the time, 2 will occur nearly 18 percent of the time, all the way on down to 9 showing up only about 5 percent of the time.
Law-abiding citizens everywhere will be happy to know our planet also obeys Benford's Law, with the duration and size of volcanic eruptions showing the same sort of pattern.
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